Construction Efficiency for Constructions of Optical Priority Queues Under Priority-Based Routing

Abstract

In our recent work [6], we have shown that the feedback system in Figure 1 (in Section I) can be operated as an optical priority queue under a simple priority-based routing policy if the conditions in (A1)-(A3) (in Section I) are satisfied. In this paper, we introduce the construction efficiency for Switched-Delay-Lines (SDL) constructions of optical priority queues to evaluate the effectiveness of SDL constructions of optical priority queues. To maximize the construction efficiency for our constructions in [6], we show that the inequalities in (A1) and (A3) should hold with equality and the buffer sizes $B_{1}, B_{2}, \\ldots, B_{k}$ in Figure 1 should satisfy the condition in (B1) (in Section II-A). We also obtain closed-form expressions or bounds for the construction efficiency for the special case that $B_{1}, B_{2}, \\ldots, B_{k}$ are given by (B2) (in Section II-A). Our results show that our construction achieves a buffer size of $2^{\\Theta(\\sqrt{M}}$ by using a feedback system consisting of an $(M+2)\\times(M+2)$ (bufferless) optical crossbar switch and $M$ fiber delay lines.